Interaction-induced phases in the half-filled Bernevig-Hughes-Zhang model in one dimension

We explore the ground-state properties of a one-dimensional model with two orbitals per site, where, in addition to atomic energies ±M and intra- and interorbital hoppings, the intraorbital Hubbard (U) and nearest-neighbor density-density (V) repulsions are included. Our results are primarily based on a Jastrow-Slater wave function and variational Monte Carlo methods but also corroborated by density-matrix renormalization group calculations. In the noninteracting limit, when varying M>0, a gapless point separates a trivial phase from a topological one. The inclusion of a finite Hubbard-U repulsion does not give rise to any phase transition within the topological region, inducing a smooth crossover into a Haldane (spin gapped) insulator; notably, the string-order parameter, which characterizes the latter phase, is already finite in the noninteracting limit. Most importantly, at finite values of U, the transition between the trivial and topological states is not direct, since an emergent insulator, which shows evidence of sustaining gapless spin excitations, intrudes between them. A small-V interaction further stabilizes the intermediate insulator, while a sufficiently large value of this nearest-neighbor repulsion gives rise to two different charge-density wave insulators, one fully gapped and another still supporting gapless spin excitations. Our results demonstrate the richness of multiorbital Hubbard models, in the presence of a topologically nontrivial band structure, and serve as a basis for future investigations on similar two-dimensional models.